Question

A researcher is interested in the effects of a psychedelic drug in treating post-traumatic stress disorder (PTSD). To assess if the psychedelic may be effective in attenuating the severity of PTSD symptoms, she performs a pilot experiment to compare the effects of the psychedelic to the commonly‑prescribed selective serotonin reuptake inhibitor (SSRI) Sertraline in individuals diagnosed with PTSD. The amount of the psychedelic was selected based on an online forum in which recreational drug users describe their drug-taking experiences. Previous research has indicated that 100 mg Sertraline is an effective amount for the general population in clinical settings. Individuals with PTSD were randomly assigned to one of two treatment conditions: Psychedelic or Sertraline. The dependent variable is a score on the PTSD Checklist (PCL); a lower score corresponds to fewer PTSD symptoms. The scores are presented in the table below.

Psychedelic Group (25 mg)		Sertraline Group (100 mg)
Subject	PCL scores	Subject	PCL scores
1	5	12	27
2	4	13	18
3	5	14	13
4	7	15	13
5	8	16	12
6	10	17	11
7	6	18	7
8	7	19	23
9	7	20	10
10	8	21	8
11	5	22	8

1. State the H₀for the experiment above. Please use appropriate notation
2. Perform the Unpaired t-test on excel. Treat the Sertraline group scores as “Variable 1” and the Psychedelic group scores as “Variable 2”. Report the results of the statistical analysis below. Be sure to include the df, the obtained statistic, and the p-value in your answer. Please round all answers to two decimal places.

1. t(_____) = _____, p = _____.
2. What do you conclude based on these results?

3. For Excel: subtract each Sertraline score from the Psychedelic score and compute the mean of these differences. Calculate standard deviation of differences using Excel function: =stdev.s. Calculate the margin of error in the confidence interval using the Excel function: =confidence.t(alpha, standard deviation, number of difference scores). Add and subtract the margin of error to and from the mean of the differences to obtain the upper and lower limits, respectively. Report the 95% confidence interval for the difference between means here: (____, ____). Are your conclusions about the 95% confidence interval consistent with the results you reported in question 2b above, and, if so, why?
4. Report the 95% confidence interval for the psychedelic group here: (____, ____).

              Report the 95% confidence interval for the sertraline group here: (____, ____).

Excel: use the =confidence.t(alpha, SD of the group, sample size) function to determine the confidence interval for each group: this will give you the margin of error. Also, compute the means of each group. Next, add and subtract the margin of error to the mean of each group to get the set of confidence limits. Inspect the confidence intervals and determine if there is a statistically significant difference between the two groups. Are these results consistent with the results you reported in question 3 above?

5. Compute the “Difference between means” in Excel by subtracting the mean of the psychedelic group from the mean of the sertraline group and p-value from the statistical test. Fill the spaces below to define the meaning of the obtained p-value and include the “Difference between means” value in your answer.

There is a ___________ probability of obtaining a mean difference at least as large as ________________ units under the condition that the null hypothesis is true.

6. According to the quick plot of the data, determine if there enough evidence/reason to claim heterogenous variances. Name the test that could be performed in the case of unequal variances. _______________________

7. Now imagine that this was a one-group, pretest-posttest design. The severity of the volunteers’ PTSD symptoms was measured using the PCL before psychedelic administration (pretest) and then afterwards (posttest). Those scores are presented below.

   Subject	Pretest	Posttest
   1	25	15
   2	24	18
   3	25	13
   4	27	13
   5	28	12
   6	30	11
   7	26	7
   8	27	23
   9	27	25
   10	28	18
   11	25	22

8. Perform paired t-test on excel. Try to achieve positive values in your results by selecting “Report differences as: by treating Pretest as “Variable 1” and Posttest as “Variable 2”. Report the results of the statistical analysis below. Be sure to include the df, the obtained statistic, and the p-value in your answer. Please round all answers to two decimal places.
9. t(_____) = _____, p = _____.
10. What do you conclude based on these results?
11. For Excel/other software users; subtract each posttest score from the pretest score and compute the mean of these differences. Use the standard deviation and confidence interval formulas above to complete this problem. Report the 95% confidence interval for the mean of differences here: (____, ____). Note: the center of this interval should be the mean of the difference. Are your conclusions about the 95% confidence interval consistent with the results you reported in question 8d above, and, if so, why?
12. Someone in the research team advises the researcher to compare the 95% confidence interval for the pretest scores to the 95% confidence interval for the posttest scores. Why is this analysis incorrect for these data? Hint: think about what is analyzed in a paired t-test.

Answer 1

Group	Group One	Group Two
Mean	6.55	13.64
SD	1.75	6.45
SEM	0.53	1.95
N	11	11

Unpaired t test results

P value and statistical significance:   The two-tailed P value equals 0.0022   By conventional criteria, this difference is considered to be very statistically significant. Confidence interval:   The mean of Group One minus Group Two equals -7.09   95% confidence interval of this difference: From -11.30 to -2.88 Intermediate values used in calculations:   t = 3.5165   df = 20   standard error of difference = 2.016

For paired t test

Group	Group One	Group Two
Mean	26.55	16.09
SD	1.75	5.61
SEM	0.53	1.69
N	11	11

P value and statistical significance:
  The two-tailed P value equals 0.0002
  By conventional criteria, this difference is considered to be extremely statistically significant.

Confidence interval:
  The mean of Group One minus Group Two equals 10.45
  95% confidence interval of this difference: From 6.31 to 14.60

Intermediate values used in calculations:
  t = 5.6195
  df = 10
  standard error of difference = 1.860